Abstract
We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator \( \mathcal{O} \) built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form \( {\mathcal{O}}^{\dagger}\mathcal{O} \), which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which \( \mathcal{O} \) condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in (1 + 1)-dimensional Anti-de Sitter space. At all temperatures, spectral functions of \( \mathcal{O} \) exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a (0 + 1)-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Green’s function of the form −i〈\( \mathcal{O} \)〉2, which is characteristic of a Kondo resonance.
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Erdmenger, J., Hoyos, C., O’Bannon, A. et al. Two-point functions in a holographic Kondo model. J. High Energ. Phys. 2017, 39 (2017). https://doi.org/10.1007/JHEP03(2017)039
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DOI: https://doi.org/10.1007/JHEP03(2017)039